What are the divisors of 2310?

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310

There is a total of 32 positive divisors.
The sum of these divisors is 6912.
The arithmetic mean is 216.

16 even divisors

2, 6, 10, 14, 22, 30, 42, 66, 70, 110, 154, 210, 330, 462, 770, 2310

16 odd divisors

1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

How to compute the divisors of 2310?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 2310 by each of the numbers from 1 to 2310 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

2310 / 1 = 2310 (the remainder is 0, so 1 is a divisor of 2310)
2310 / 2 = 1155 (the remainder is 0, so 2 is a divisor of 2310)
2310 / 3 = 770 (the remainder is 0, so 3 is a divisor of 2310)
...
2310 / 2309 = 1.0004330879168 (the remainder is 1, so 2309 is not a divisor of 2310)
2310 / 2310 = 1 (the remainder is 0, so 2310 is a divisor of 2310)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 2310 (i.e. 48.062459362792). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

2310 / 1 = 2310 (the remainder is 0, so 1 and 2310 are divisors of 2310)
2310 / 2 = 1155 (the remainder is 0, so 2 and 1155 are divisors of 2310)
2310 / 3 = 770 (the remainder is 0, so 3 and 770 are divisors of 2310)
...
2310 / 47 = 49.148936170213 (the remainder is 7, so 47 is not a divisor of 2310)
2310 / 48 = 48.125 (the remainder is 6, so 48 is not a divisor of 2310)